2 problems

Torus conjecture. The complex $X_{A_{\mathcal{X}}}$ is homotopic to a real torus $\mathbb{T}$.

The Fulton–MacPherson operad is the operad ${\operatorname{FM}}_2=\bigl({\operatorname{FM}}_2(k)\bigr)_{k\geq1}$, whose $k$-ary space compactifies configurations of $k$ distinct la…